Question

How do you simplify $4\left( fg+3g \right)+5g$?

Answer 1

Hint: In this problem we will use the BODMAS rule which states the order of operations of different operators. From the BODMAS rule we need to solve the division part, there by multiplication part and then subtraction part and finally addition part. So, we will check which operations are given in the given equation and apply the arithmetic properties like distribution law of multiplication and so on. By using all those laws and the BODMAS rule we will get a value as a result. Now we can take the term $g$ as common to get a more simplified result.

Complete step by step answer:
Given $4\left( fg+3g \right)+5g$.
In the above equation we have only two operations they are Multiplication and addition. From the BODMAS rule we need to do multiplication first and then addition in the given problem.
Expanding the term $4\left( fg+3g \right)$ by using distribution law of multiplication, then we will get
$\begin{align}
  & 4\left( fg+3g \right)+5g=4fg+4\times 3g+5g \\
 & \Rightarrow 4\left( fg+3g \right)+5g=4fg+12g+5g \\
\end{align}$
Now doing the addition operation for the suitable variables, then we will get
$\Rightarrow 4\left( fg+3g \right)+5g=4fg+17g$
Taking $g$ common from the above equation, then we will get
$\Rightarrow 4\left( fg+3g \right)+5g=\left( 4f+17 \right)g$

Hence the simplified form of $4\left( fg+3g \right)+5g$ is $\left( 4f+17 \right)g$.

Note: In the problem there is a chance of making mistakes at the addition part. We know that we can only add the terms of similar type only. So, we have added $5g$ to $12g$. But don’t add all the terms or any other two terms except $5g$ to $12g$ it’s completely mathematically wrong.